Block #922,497

1CCLength 10★★☆☆☆

Cunningham Chain of the First Kind · Discovered 2/4/2015, 12:52:16 PM · Difficulty 10.9152 · 5,885,615 confirmations

1CC
Cunningham Chain of the First Kind

A sequence where each prime is double the previous prime plus one.

Block Header
Block Hash
95713875a75d588519cc8050d38df5240238c68e7a4dae17c53da843ed145fac

Height

#922,497

Difficulty

10.915221

Transactions

5

Size

116.09 KB

Version

2

Bits

0aea4be7

Nonce

313,210,627

Timestamp

2/4/2015, 12:52:16 PM

Confirmations

5,885,615

Merkle Root

076091de53b1a1d648dabbb26a6f0a2fd1ac451b2fe1f2499f508feb08278f67
Transactions (5)
1 in → 1 out9.5800 XPM116 B
200 in → 1 out900.8650 XPM28.97 KB
200 in → 1 out1001.6946 XPM28.97 KB
200 in → 1 out959.5930 XPM28.97 KB
200 in → 1 out1013.9317 XPM28.97 KB
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

2.483 × 10⁹⁷(98-digit number)
24838134955912217028…81202545960371615999
Discovered Prime Numbers
p_k = 2^k × origin − 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

1
origin − 1
2.483 × 10⁹⁷(98-digit number)
24838134955912217028…81202545960371615999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
2
2^1 × origin − 1
4.967 × 10⁹⁷(98-digit number)
49676269911824434056…62405091920743231999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
3
2^2 × origin − 1
9.935 × 10⁹⁷(98-digit number)
99352539823648868113…24810183841486463999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
4
2^3 × origin − 1
1.987 × 10⁹⁸(99-digit number)
19870507964729773622…49620367682972927999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
5
2^4 × origin − 1
3.974 × 10⁹⁸(99-digit number)
39741015929459547245…99240735365945855999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
6
2^5 × origin − 1
7.948 × 10⁹⁸(99-digit number)
79482031858919094490…98481470731891711999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
7
2^6 × origin − 1
1.589 × 10⁹⁹(100-digit number)
15896406371783818898…96962941463783423999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
8
2^7 × origin − 1
3.179 × 10⁹⁹(100-digit number)
31792812743567637796…93925882927566847999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
9
2^8 × origin − 1
6.358 × 10⁹⁹(100-digit number)
63585625487135275592…87851765855133695999
Verify on FactorDB ↗Wolfram Alpha ↗
×2+1 →
10
2^9 × origin − 1
1.271 × 10¹⁰⁰(101-digit number)
12717125097427055118…75703531710267391999
Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Cunningham Chain of the First Kind. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★☆☆☆
Rarity
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)
Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the 1CC formula:

1CC: p₁ (first prime), p₂ = 2p₁ + 1, p₃ = 2p₂ + 1, …
Circulating Supply:57,708,943 XPM·at block #6,808,111 · updates every 60s
xpmprime.info is a work in progress. If you enjoy using this service you can support this project with a Primecoin donation.

Cookie Preferences

We use cookies to enhance your experience. Some are essential for the site to function, while others help us understand how you use the site.

·Privacy Policy